Large displacement analysis of shear deformable composite beams with interlayer slips

Abstract

This paper presents a novel geometric non-linear finite element formulation for the analysis of shear deformable two-layer beams with interlayer slips. We adopt the co-rotational approach where the motion of the element is decomposed into two parts: a rigid body motion which defines a local coordinate system and a small deformational motion of the element relative to this local coordinate system. The main advantage of this approach is that the transformation matrices relating local and global quantities are independent to the choice of the geometrical linear local element. The effect of transverse shear deformation of the layers is taken into account by assuming that each layer behaves as a Timoshenko beam element. The layers are assumed to be continuously connected and partial interaction is considered by considering a continuous relationship between the interface shear flow and the corresponding slip. In order to avoid curvature and shear locking phenomena, the local linear element is formulated using “exact” displacement shape functions derived from the closed-form solution of the governing equations of a two-layer beam element. Finally, three numerical applications are presented in order to assess the performance of the proposed formulation.